I do not think that their is energy in space because, everything is floats because of gravity. So it's matter which takes its place and, gravitation !!! Hope this helps
It lasts 29 1/2 days.
-the sidereal month- is the true period of the moon's revolution around Earth. It lasts 27 1/3 days.
-the difference of 2 days between the synodic and sidereal cycles is due to the Earth- moon system also moving in an orbit around the sun.
Answer:
a)
, b)
,
, ![\phi = -0.473\pi](https://tex.z-dn.net/?f=%5Cphi%20%3D%20-0.473%5Cpi)
Explanation:
a) The system mass-spring is well described by the following equation of equilibrium:
![\Sigma F = k\cdot x - m\cdot g = m\cdot a](https://tex.z-dn.net/?f=%5CSigma%20F%20%3D%20k%5Ccdot%20x%20-%20m%5Ccdot%20g%20%3D%20m%5Ccdot%20a)
After some handling in physical and mathematical definition, the following non-homogeneous second-order linear differential equation:
The solution of this equation is:
![x (t) = A\cdot \cos \left(\sqrt{\frac{k}{m} } \cdot t + \phi\right)](https://tex.z-dn.net/?f=x%20%28t%29%20%3D%20A%5Ccdot%20%5Ccos%20%5Cleft%28%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%20%5Ccdot%20t%20%2B%20%5Cphi%5Cright%29)
The velocity function is:
![v(t) = \sqrt{\frac{k}{m} }\cdot A\cdot \sin \left(\sqrt{\frac{k}{m} }\cdot t +\phi \right)](https://tex.z-dn.net/?f=v%28t%29%20%3D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%5Ccdot%20A%5Ccdot%20%5Csin%20%5Cleft%28%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%5Ccdot%20t%20%2B%5Cphi%20%20%5Cright%29)
Initial conditions are:
![x(0\,s) = 0.25\,ft, v(0\,s) = -5\,\frac{ft}{s}](https://tex.z-dn.net/?f=x%280%5C%2Cs%29%20%3D%200.25%5C%2Cft%2C%20v%280%5C%2Cs%29%20%3D%20-5%5C%2C%5Cfrac%7Bft%7D%7Bs%7D)
Equations at
are:
![0.25\,ft = A\cdot \cos \phi\\-5\,\frac{ft}{s} =\sqrt{\frac{k}{m} }\cdot A\cdot \sin \phi](https://tex.z-dn.net/?f=0.25%5C%2Cft%20%3D%20%20A%5Ccdot%20%5Ccos%20%5Cphi%5C%5C-5%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%3D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%5Ccdot%20A%5Ccdot%20%5Csin%20%5Cphi)
The spring constant is:
![k = \frac{11\,lbf}{0.333\,ft}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B11%5C%2Clbf%7D%7B0.333%5C%2Cft%7D)
![k = 33\,\frac{lbf}{ft}](https://tex.z-dn.net/?f=k%20%3D%2033%5C%2C%5Cfrac%7Blbf%7D%7Bft%7D)
After some algebraic handling, amplitude and phase angle are found:
![\phi = -0.473\pi](https://tex.z-dn.net/?f=%5Cphi%20%3D%20-0.473%5Cpi)
![A = 2.845\,ft](https://tex.z-dn.net/?f=A%20%3D%202.845%5C%2Cft)
The position can be described by this function:
![x(t) = 2.845\cdot \cos \left(1.732\cdot t -0.473\pi \right)](https://tex.z-dn.net/?f=x%28t%29%20%3D%202.845%5Ccdot%20%5Ccos%20%5Cleft%281.732%5Ccdot%20t%20-0.473%5Cpi%20%5Cright%29)
b) The period of the motion is:
![T = \frac{2\pi}{\sqrt{\frac{k}{m} } }](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D%20%7D)
![T = 3.628\,s](https://tex.z-dn.net/?f=T%20%3D%203.628%5C%2Cs)
The amplitude is:
![A = 2.845\,ft](https://tex.z-dn.net/?f=A%20%3D%202.845%5C%2Cft)
The phase of the motion is:
![\phi = -0.473\pi](https://tex.z-dn.net/?f=%5Cphi%20%3D%20-0.473%5Cpi)
Reactivity is the ability of matter that allows it to easily chemically combine with other substances.
Answer:
0.8 m/s
Explanation:
F(avg) * Δt = I, where
F(avg) = Average force
Δt = change in time
I = impulse
From the question, we know that the
average force is given as -17600 N
time change is given as 55 milliseconds
speed of the player, v = 8 m/s
Mass of the player is given as 110 kg
Impulse, I = F(avg) * Δt
I = -17600 * 0.055
I = -968
Now, using the Impulse-Momentum theory, we have that
Δp = I and thus,
Δp = m [v(f) - v(i)], where
Δp = change in the momentum
v(f) = final speed of the player
v(i) = initial speed of the player
Substituting the values, we have
I = m [v(f) - v(i)]
-968 = m.v(f) - m.v(i)
m.v(f) = m.v(i) - 968
110v(f) = 110 * 8 - 968
110v(f) = 880 - 968
110v(f) = -88
v(f) = -88 / 110
v(f) = -0.8 m/s